Question: Simplify the following expression: $\dfrac{144a^5}{72a}$ You can assume $a \neq 0$.
$ \dfrac{144a^5}{72a} = \dfrac{144}{72} \cdot \dfrac{a^5}{a} $ To simplify $\frac{144}{72}$ , find the greatest common factor (GCD) of $144$ and $72$ $144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(144, 72) = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 72 $ $ \dfrac{144}{72} \cdot \dfrac{a^5}{a} = \dfrac{72 \cdot 2}{72 \cdot 1} \cdot \dfrac{a^5}{a} $ $\phantom{ \dfrac{144}{72} \cdot \dfrac{5}{1}} = 2 \cdot \dfrac{a^5}{a} $ $ \dfrac{a^5}{a} = \dfrac{a \cdot a \cdot a \cdot a \cdot a}{a} = a^4 $ $ 2 \cdot a^4 = 2a^4 $